Greene played baseball at Whiteville High School in North Carolina where he was teammates with Patrick Lennon and won a state championship.

Greene became the first visiting pitcher to hurl a no-hitter in Montreal's history as the Phillies defeated the Expos, 2–0 before an Olympic Stadium crowd of 8,833.

[2] The next year in 1992, tendonitis in his arm and shoulder caused him to miss 3+1⁄2 months of the season; he appeared in only 13 games.

He was chased out early in a rout loss in Game 2 but bounced back with seven solid innings in the latter that saw Philadelphia win its first pennant in ten years.

[3] Greene was a GM of the Southern Collegiate baseball team, the Monroe Channel Cats, and also maintains a real estate business.